Question 970061
{{{6/(x-3)< 3/(x+1)}}}


{{{6/(x-3)-3/(x+1)<0}}}


{{{2/(x-3)-1/(x+1)<0}}}


{{{(2(x+1)-(x-3))/((x-3)(x+1))<0}}}


{{{(2x+2-x+3)/((x-3)(x+1))<0}}}


{{{highlight((x+5)/((x-3)(x+1))<0)}}}

Critical values of x are -5,-1,3.
These make four intervals on the x-axis number line.  Pick any value INSIDE each interval and check for truth or falseness for the inequality statement.


The intervals within to check are these:
{{{x<-5}}}
-
{{{-5<x<-1}}}
-
{{{-1<x<3}}}
-
{{{3<x}}}